Calculate the time taken for a car to cover a distance of 100m if the initial speed is 10km/h and it has a constant acceleration of 1.5m/s2?

1 Answer
May 30, 2018

#"9.843 seconds"#

Explanation:

#10 {km}/h = 10/3.6 m/s = 25/9 m/s#
#x = v_0 * t + a * t^2/2#
#=> 100 = (25/9)*t + 1.5*t^2/2#
#"This is a quadratic equation in t, we solve it :"#
#=> 3600 = 100*t + 27*t^2#
#=> 27*t^2 + 100*t - 3600 = 0#
#"discriminant : "100^2 + 3600*4*27 = 398800 = 631.5^2#
#=> t = (-100 pm 631.5)/54#
#"we have to take the solution with the + sign as t > 0."#
#=> t = 531.5/54 = 9.843 s#